Strasburg (4-2) allowed two base runners in each of the first three innings, walking three and throwing the first wild pitch of his career. He finished with seven strikeouts in six innings and lowered his ERA to 2.03. Two relievers completed a four-hitter.
The shutout was the third this season for the Nationals, thanks in part to Strasburg's first scoreless outing.
Making his eighth major league start and facing Florida for the first time, Strasburg was locked in a scoreless duel with Ricky Nolasco (9-7) until Josh Willingham hit a three-run double in the sixth.
At St. Louis, Yadier Molina homered and drove in four runs as St. Louis overcame a rough start by rookie Jaime Garcia to beat Los Angeles.
Chad Billingsley (7-5) was the second straight Dodgers starter to get roughed up by the Cardinals, allowing seven runs and 10 hits in four innings. It was the second-shortest outing of the season for the right-hander, who has a 1.09 ERA in four-day games but a 5.76 ERA in 13 night starts.
Randy Winn added two hits and two RBIs, his first since June 13, off a pitcher he's batting .481 against (13 for 27) with seven RBIs. Winn got a spot start in right field ahead of rookie Jon Jay, who's batting .500 during a 12-game hitting streak.
James Loney had three hits and an RBI for the Dodgers, who are 3-13 at 5-year-old Busch Stadium. Rafael Furcal, a .342 career hitter against the Cardinals, had two hits and a bases-loaded walk, and was robbed of a third hit by second baseman Skip Schumaker's diving stab in the third.
The Dodgers had 13 hits but stranded 12 runners, going 3 for 17 with runners in scoring position.
Garcia, one of the National League's top rookie pitchers at 8-4 with a 2.27 ERA, labored through 3 1-3 innings, allowing two runs and eight hits. In his last two outings, he has allowed 17 hits and five earned runs in 8 2-3 innings.
At Cincinnati, Brandon Phillips followed his first All-Star appearance with a three-hit game and first-time All-Star Arthur Rhodes pitched out of a bases-loaded, no-outs threat in the eighth inning as Cincinnati beat Colorado.
The NL Central leaders hadn't played a home game all month and had dropped five of its last six on the road.
Bronson Arroyo (10-4) gave up a solo homer by Miguel Olivo that was upheld after a review and cut it to 3-2 in the eighth.
Phillips scored twice and had three hits off Jason Hammel (7-4), who had won his last six decisions. Hammel struck out a career-high 10.
The victory was a breakthrough for Cincinnati, which had lost its last nine games against Colorado and is 4-16 against the Rockies since 2007.
At San Diego, All-Star slugger Adrian Gonzalez hit a two-run homer to key a five-run outburst and Jon Garland threw six strong innings as the San Diego Padres routed the Arizona Diamondbacks.
Gonzalez put the NL West leaders ahead 2-1 in the fourth when he connected off Dan Haren (7-8) for his 19th homer.
San Diego added three more runs in the inning.
Garland (9-6) finally beat the Diamondbacks after having tough luck in his first two starts against them this season. The right-hander allowed one run and three hits with five strikeouts and two walks. He combined with three relievers on a four-hitter.
In his two previous outings against the Diamondbacks, including an opening-day 6-3 loss at Arizona, Garland had gone 0-1 while allowing seven unearned runs.
San Diego increased its lead in the NL West to three games over the Colorado Rockies, 3-2 losers at Cincinnati.
Arizona has lost eight of 10 to drop 18 1/2 games behind the Padres.
After David Eckstein led off the fourth with a double, Gonzalez connected against Haren on an 0-1 pitch off the outside part of the plate to drive the ball into the left-field stands. The ball barely made it over the wall into the front row.
Headley followed with a double and went to third on Nick Hundley's single. One out later, Aaron Cunningham hit a sacrifice fly. A walk and an infield single by Garland loaded the bases before Jerry Hairston Jr. singled in two runs for a 5-1 lead.
Headley added a homer off Haren, his seventh, in the fifth.
Haren gave up six runs and eight hits over five innings.
The right-hander, who struck out eight and walked one, is 0-4 in his last six starts with a 4.57 ERA.
At San Francisco, Barry Zito struck out 10 in eight dominant innings of two-hit ball and the San Francisco Giants shut out New York for the second consecutive game.
All-Star closer Brian Wilson completed the three-hitter for San Francisco, which has won four straight and nine of 11. Aubrey Huff had three hits and scored the only run on a fielder's choice grounder.
Zito (8-4) matched his season high for strikeouts and allowed only one runner past first base while winning for the first time in more than a month. The left-hander faced just three batters more than the minimum before Wilson earned his 24th save.
Despite the return of cleanup batter Carlos Beltran, the Mets haven't scored in two games since the All-Star break.
Both times, they faced a Cy Young Award winner.
Jonathon Niese was the hard-luck loser for New York, shut out for the third time in the last four games. The Mets have scored nine runs in their last seven, going 2-5 during that stretch.
Zito hadn't made it out of the sixth inning in his previous four starts but was in control while keeping New York's offense quiet. His performance, coming on the heels of Tim Lincecum's six-hit gem Thursday night, ended a streak of three straight no-decisions for the Giants' lefty and gave him his first win since Zito beat his former team, Oakland, on June 12.
Mets manager Jerry Manuel tried shaking up his lineup, moving left fielder Jason Bay to second in the batting order, but it didn't matter against Zito.
At Pittsburgh, Jeff Keppinger homered and had three RBIs and Brett Myers allowed two runs while working into the eighth inning as Houston remained unbeaten in seven games against Pittsburgh this season.
Myers (7-6) extended his club record for consecutive starts of at least six innings to begin a season to 19, allowing two runs and five hits in 7 2-3 innings, striking out four and walking one.
Andrew McCutchen went 2 for 4 with an RBI and a run for Pittsburgh, which has lost seven consecutive overall.
At Chicago, Aramis Ramirez homered with two outs in the eighth inning - his third hit of the game - to cap Chicago's rally past Philadelphia.
Ramirez's 11th homer came off Ryan Madson (2-1) and gave him 14 RBIs in his last eight games.
Ryan Howard hit his 20th homer with two outs in the sixth, his third home run in two games and it put the Phils up 3-1.
The Cubs scored two runs in the bottom of the inning with a two-out rally off Joe Blanton as Ramirez doubled and Marlon Byrd followed with his 10th homer.
Shane Victorino also homered for the Phillies.
At Atlanta, Ryan Braun's two-run homer helped Milwaukee to an early lead and Randy Wolf earned his first win over Atlanta in seven years.
Wolf (7-8) allowed seven hits and three runs in six innings for his first win over the Braves since Sept. 9, 2003, also at Turner Field. Wolf improved to 5-12 in his career against Atlanta.
Prince Fielder had a two-run double in the Brewers' three-run eighth. Milwaukee had 16 hits, including five off Kenshin Kawakami in the eighth.
Casey McGehee had three hits, including a run-scoring single in the eighth.
Alcides Escobar drove in McGehee with a single in the second. Wolf added a sacrifice fly for a 2-0 lead. After Corey Hart led off the third with a single, Braun's homer made it 4-0.
